Average Error: 7.9 → 2.0
Time: 5.4s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{x}{y - z}}{t - z}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{x}{y - z}}{t - z}
double f(double x, double y, double z, double t) {
        double r816418 = x;
        double r816419 = y;
        double r816420 = z;
        double r816421 = r816419 - r816420;
        double r816422 = t;
        double r816423 = r816422 - r816420;
        double r816424 = r816421 * r816423;
        double r816425 = r816418 / r816424;
        return r816425;
}
↓
double f(double x, double y, double z, double t) {
        double r816426 = x;
        double r816427 = y;
        double r816428 = z;
        double r816429 = r816427 - r816428;
        double r816430 = r816426 / r816429;
        double r816431 = t;
        double r816432 = r816431 - r816428;
        double r816433 = r816430 / r816432;
        return r816433;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.9
Target8.7
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.9

    \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  2. Using strategy rm

  3. Applied associate-/r*2.0

    \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}}\]

  4. Final simplification2.0

    \[\leadsto \frac{\frac{x}{y - z}}{t - z}\]

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))